As depicted in figure REF , our simulation domain consists of a three-dimensional rectangular box of dimensions \(27D \times D \times D\) , corresponding to the \(x\)  (channel length), \(y\)  (channel height), and \(z\)  (channel width)-directions, respectively. The value of the channel length was selected to ensure the attainment of a steady-state bubble propagation for \(We < 10\) , following the results of [1]} and [2]}. Under conditions of \(We > 10\) , highly unsteady encapsulation/bursting phenomena are detected in the system. The channel length chosen allowed for the observation of all relevant phenomena, including the formation of the liquid cavity, drop encapsulations and coalescence events, and bubble bursting, for all conditions tested. The elongated bubble was initialised in quiescent conditions close to the channel inlet and at the centre-line of the \(y\)  and \(z\) -directions as a horizontal cylinder of length \(3.12D\)  with two hemispherical caps of diameter \(0.94D\)  on each end. A fully-developed liquid velocity profile was imposed at the channel inlet with a Neumann condition for pressure (\(\partial p/\partial \textbf {n} = 0\) ). All walls were treated as no-slip boundaries, and Neumann conditions were imposed for all variables at the outlet. The bubble-liquid interface was initially covered in surfactant with uniform concentration \(\Gamma _{0}\) , determined from an initial equilibrium state between surfactant adsorption and desorption (last term on the RHS of Eq. (REF ) equal to zero), which, assuming \(C_{s} = C_{\infty }\)  initially, reads as:
\(\begin{split}\Gamma _{0} = \frac{k}{k+1}\Gamma _{\infty }.\end{split}\) 
